Question

The R.M.S. speed of the molecules of a gas of density $4{\text{kg m}}^{-3}$ and pressure $1.2\times {10}^5{\text{N m}}^{-2}$ is:

• A. $120{\text{ms}}^{-1}$
  
• B. $300{\text{ms}}^{-1}$
  
• C. $600{\text{ms}}^{-1}$
  
• D. $900{\text{ms}}^{-1}$
  

Answer 1

The correct option is B $300{\text{ms}}^{-1}$


As we know,
$U_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3P}{d}}$
Here, pressure $\left(P\right)=1.2\times {10}^5{\text{N m}}^{-2}$
Density $\left(d\right)=4{\text{kg m}}^{-3}$

$\therefore U_{rms}=\sqrt{\frac{3\times 1.2\times {10}^5}{4}}$
$=3\times {10}^2{\text{ms}}^{-1}$
$=300{\text{ms}}^{-1}$.